Book

Digital
Processing
Optical Transmission and
Coherent Receiving Techniques

Optics and Photonics
Series Editor
Le Nguyen Binh
Huawei Technologies, European Research Center, Munich, Germany
1. Digital Optical Communications, Le Nguyen Binh
2. Optical Fiber Communications Systems: Theory and Practice with MATLAB®
and
Simulink®
Models, Le Nguyen Binh
3. Ultra-Fast Fiber Lasers: Principles and Applications with MATLAB®
Models,
Le Nguyen Binh and Nam Quoc Ngo
4. Thin-Film Organic Photonics: Molecular Layer Deposition and Applications,
Tetsuzo Yoshimura
5. Guided Wave Photonics: Fundamentals and Applications with MATLAB®
,
Le Nguyen Binh
6. Nonlinear Optical Systems: Principles, Phenomena, and Advanced Signal
Processing, Le Nguyen Binh and Dang Van Liet
7. Wireless and Guided Wave Electromagnetics: Fundamentals and Applications,
Le Nguyen Binh
8. Guided Wave Optics and Photonic Devices, Shyamal Bhadra and Ajoy Ghatak

CRC Press is an imprint of the
Taylor & Francis Group, an informa business
Boca Raton London NewYork
Digital
Processing
Optical Transmission and
Coherent Receiving Techniques
Le Nguyen Binh

MATLAB® and Simulink® are trademarks of The MathWorks, Inc. and are used with permission. The Math-
Works does not warrant the accuracy of the text or exercises in this book. This book’s use or discussion
of MATLAB® and Simulink® software or related products does not constitute endorsement or sponsorship
by The MathWorks of a particular pedagogical approach or particular use of the MATLAB® and Simulink®
software.
CRC Press
Taylor & Francis Group
6000 Broken Sound Parkway NW, Suite 300
Boca Raton, FL 33487-2742
© 2014 by Taylor & Francis Group, LLC
CRC Press is an imprint of Taylor & Francis Group, an Informa business
No claim to original U.S. Government works
Version Date: 20130916
International Standard Book Number-13: 978-1-4665-0671-8 (eBook - PDF)
This book contains information obtained from authentic and highly regarded sources. Reasonable efforts
have been made to publish reliable data and information, but the author and publisher cannot assume
responsibility for the validity of all materials or the consequences of their use. The authors and publishers
have attempted to trace the copyright holders of all material reproduced in this publication and apologize to
copyright holders if permission to publish in this form has not been obtained. If any copyright material has
not been acknowledged please write and let us know so we may rectify in any future reprint.
Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmit-
ted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented,
including photocopying, microfilming, and recording, or in any information storage or retrieval system,
without written permission from the publishers.
For permission to photocopy or use material electronically from this work, please access www.copyright.
com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood
Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and
registration for a variety of users. For organizations that have been granted a photocopy license by the CCC,
a separate system of payment has been arranged.
Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used
only for identification and explanation without intent to infringe.
Visit the Taylor & Francis Web site at
http://www.taylorandfrancis.com
and the CRC Press Web site at
http://www.crcpress.com

v
Contents
Preface......................................................................................................................xv
Author.................................................................................................................... xix
Abbreviations....................................................................................................... xxi
1 Overview of Optical Fiber Communications and DSP-Based
Transmission Systems....................................................................................1
1.1 Introduction............................................................................................1
1.2 From Few Mb/s to Tb/s: Transmission and Receiving
for Optical Communications Systems��3
1.2.1 Guiding Lightwaves over the Last 40 Years.........................3
1.2.2 Guiding Lightwaves: Single Mode, Multimode, and
Few Mode...................................................................................8
1.2.3 Modulation Formats: Intensity to Phase Modulation,
Direct to External Modulation��8
1.2.4 Coherent and Incoherent Receiving Techniques..................9
1.2.5 Digital Processing in Advanced Optical
Communication Systems....................................................... 10
1.3 Digital Modulation Formats............................................................... 11
1.3.1 Modulation Formats............................................................... 11
1.3.2 Pulse Shaping and Modulations for High Spectral
Efficiency..................................................................................13
1.3.2.1 Partial Response......................................................13
1.3.2.2 Nyquist Pulse Shaping...........................................15
1.4 Optical Demodulation: Phase and Polarization
Diversity Technique��18
1.5 Organization of the Book Chapters...................................................23
References........................................................................................................24
2 Optical Fibers: Guiding and Propagation Properties............................25
2.1 Optical Fibers: Circular Optical Waveguides..................................25
2.1.1 General Aspects......................................................................25
2.1.2 Optical Fiber: General Properties.........................................26
2.1.2.1 Geometrical Structures and Index Profile...........26
2.1.3 Fundamental Mode of Weakly Guiding Fibers..................29
2.1.3.1 Solutions of the Wave Equation for
Step-Index Fiber��30
2.1.3.2 Single and Few Mode Conditions.........................31
2.1.3.3 Gaussian Approximation: Fundamental
Mode Revisited........................................................36
2.1.3.4 Cut-Off Properties...................................................38

vi Contents
2.1.3.5 Power Distribution..................................................40
2.1.3.6 Approximation of Spot-Size r0 of a
Step-Index Fiber��41
2.1.4 Equivalent-Step Index Description......................................41
2.2 Nonlinear Optical Effects...................................................................42
2.2.1 Nonlinear Self-Phase Modulation Effects...........................42
2.2.2 Self-Phase Modulation...........................................................43
2.2.3 Cross-Phase Modulation........................................................44
2.2.4 Stimulated Scattering Effects................................................45
2.2.4.1 Stimulated Brillouin Scattering.............................46
2.2.4.2 Stimulated Raman Scattering................................47
2.2.4.3 Four-Wave Mixing Effects.....................................48
2.3 Signal Attenuation in Optical Fibers.................................................49
2.3.1 Intrinsic or Material Absorption Losses..............................49
2.3.2 Waveguide Losses...................................................................50
2.3.3 Attenuation Coefficient..........................................................52
2.4 Signal Distortion in Optical Fibers....................................................53
2.4.1 Material Dispersion................................................................55
2.4.2 Waveguide Dispersion...........................................................58
2.4.2.1 Alternative Expression for Waveguide
Dispersion Parameter............................................. 61
2.4.2.2 Higher-Order Dispersion.......................................62
2.4.3 Polarization Mode Dispersion..............................................63
2.5 Transfer Function of Single-Mode Fibers.........................................65
2.5.1 Linear Transfer Function.......................................................65
2.5.2 Nonlinear Fiber Transfer Function......................................72
2.5.3 Transmission Bit Rate and the Dispersion Factor..............77
2.6 Fiber Nonlinearity Revisited..............................................................78
2.6.1 SPM, XPM Effects...................................................................78
2.6.2 SPM and Modulation Instability..........................................80
2.6.3 Effects of Mode Hopping.......................................................81
2.6.4 SPM and Intra-Channel Nonlinear Effects.........................81
2.6.5 Nonlinear Phase Noises.........................................................86
2.7 Special Dispersion Optical Fibers......................................................87
2.8 SMF Transfer Function: Simplified Linear and Nonlinear
Operating Region��88
2.9 Numerical Solution: Split-Step Fourier Method..............................95
2.9.1 Symmetrical Split-Step Fourier Method..............................95
2.9.1.1 Modeling of Polarization Mode Dispersion........97
2.9.1.2 Optimization of Symmetrical SSFM....................98
2.10 Nonlinear Fiber Transfer Functions and Compensations
in Digital Signal Processing��99
2.10.1 Cascades of Linear and Nonlinear Transfer
Functions in Time and Frequency Domains�� 101

viiContents
2.10.2 Volterra Nonlinear Transfer Function and Electronic
Compensation�� 103
2.10.3 Inverse of Volterra Expansion and Nonlinearity
Compensation in Electronic Domain�� 104
2.10.3.1 Inverse of Volterra Transfer Function................. 106
2.10.3.2 Electronic Compensation Structure................... 108
2.10.3.3 Remarks.................................................................. 111
2.10.4 Back-Propagation Techniques for Compensation of
Nonlinear Distortion�� 111
2.11 Concluding Remarks......................................................................... 114
References...................................................................................................... 115
3 External Modulators for Coherent Transmission and Reception...... 121
3.1 Introduction........................................................................................ 121
3.2 External Modulation and Advanced Modulation Formats.........122
3.2.1 Electro-Absorption Modulators..........................................122
3.2.2 Electro-Optic Modulators.................................................... 124
3.2.2.1 Phase Modulators..................................................125
3.2.2.2 Intensity Modulators............................................125
3.2.2.3 Phasor Representation and Transfer
Characteristics.......................................................127
3.2.2.4 Bias Control............................................................128
3.2.2.5 Chirp-Free Optical Modulators..........................129
3.2.2.6 Structures of Photonic Modulators.....................130
3.2.2.7 Typical Operational Parameters.......................... 131
3.2.3 ASK Modulation Formats and Pulse Shaping.................. 131
3.2.3.1 Return-to-Zero Optical Pulses............................ 131
3.2.3.2 Phasor Representation..........................................134
3.2.3.3 Phasor Representation of CSRZ Pulses..............135
3.2.3.4 Phasor Representation of RZ33 Pulses..............136
3.2.4 Differential Phase Shift Keying.......................................... 137
3.2.4.1 Background............................................................ 137
3.2.4.2 Optical DPSK Transmitter...................................138
3.3 Generation of Modulation Formats................................................. 140
3.3.1 Amplitude Modulation ASK-NRZ and ASK-RZ.............. 140
3.3.2 Amplitude Modulation Carrier-Suppressed RZ
Formats................................................................................... 141
3.3.3 Discrete Phase Modulation NRZ Formats........................ 141
3.3.3.1 Differential Phase Shift Keying.......................... 141
3.3.3.2 Differential Quadrature Phase Shift Keying......143
3.3.3.3 Non Return-to-Zero Differential Phase
Shift Keying........................................................... 143
3.3.3.4 Return-to-Zero Differential Phase Shift
Keying..................................................................... 143

viii Contents
3.3.3.5 Generation of M-Ary Amplitude
Differential Phase Shift Keying
(M-Ary ADPSK) Using One MZIM.................... 144
3.3.3.6 Continuous Phase Modulation PM-NRZ
Formats................................................................... 146
3.3.3.7 Linear and Nonlinear MSK................................. 147
3.4 Photonic MSK Transmitter Using Two Cascaded Electro-
Optic Phase Modulators.................................................................... 151
3.4.1 Configuration of Optical MSK Transmitter Using
Mach–Zehnder Intensity Modulators: I–Q Approach.....153
3.4.2 Single-Side Band Optical Modulators................................155
3.4.3 Optical RZ-MSK....................................................................156
3.4.4 Multi-Carrier Multiplexing Optical Modulators..............156
3.4.5 Spectra of Modulation Formats.......................................... 159
3.5 I–Q Integrated Modulators...............................................................164
3.5.1 Inphase and Quadrature Phase Optical
Modulators.............................................................................164
3.5.2 IQ Modulator and Electronic Digital Multiplexing
for Ultra-High Bit Rates....................................................... 167
3.6 DAC for DSP-Based Modulation and Transmitter........................ 168
3.6.1 Fujitsu DAC............................................................................ 168
3.6.2 Structure................................................................................. 170
3.6.2.1 Generation of I and Q Components.................... 171
3.7 Remarks............................................................................................... 173
References...................................................................................................... 176
4 Optical Coherent Detection and Processing Systems.......................... 179
4.1 Introduction........................................................................................ 179
4.2 Coherent Receiver Components....................................................... 181
4.3 Coherent Detection............................................................................ 182
4.3.1 Optical Heterodyne Detection............................................ 185
4.3.1.1 ASK Coherent System........................................... 187
4.3.1.2 PSK Coherent System........................................... 189
4.3.1.3 Differential Detection...........................................190
4.3.1.4 FSK Coherent System............................................ 191
4.3.2 Optical Homodyne Detection............................................. 192
4.3.2.1 Detection and OPLL.............................................. 193
4.3.2.2 Quantum Limit Detection................................... 194
4.3.2.3 Linewidth Influences............................................ 195
4.3.3 Optical Intradyne Detection................................................200
4.4 Self-Coherent Detection and Electronic DSP.................................201
4.5 Electronic Amplifiers: Responses and Noises...............................203
4.5.1 Introduction...........................................................................203
4.5.2 Wideband TIAs.....................................................................205
4.5.2.1 Single Input/Single Output.................................205

ixContents
4.5.2.2 Differential Inputs, Single/Differential
Output.....................................................................205
4.5.3 Amplifier Noise Referred to Input.....................................206
4.6 Digital Signal Processing Systems and Coherent
Optical Reception��208
4.6.1 DSP-Assisted Coherent Detection......................................208
4.6.1.1 DSP-Based Reception Systems............................209
4.6.2 Coherent Reception Analysis.............................................. 211
4.6.2.1 Sensitivity............................................................... 211
4.6.2.2 Shot-Noise-Limited Receiver Sensitivity........... 215
4.6.2.3 Receiver Sensitivity under Nonideal
Conditions.............................................................. 216
4.6.3 Digital Processing Systems.................................................. 217
4.6.3.1 Effective Number of Bits...................................... 218
4.6.3.2 Impact of ENOB on Transmission
Performance...........................................................226
4.6.3.3 Digital Processors..................................................228
4.7 Concluding Remarks.........................................................................228
4.8 Appendix: A Coherent Balanced Receiver and Method
for Noise Suppression........................................................................231
4.8.1 Analytical Noise Expressions.............................................233
4.8.2 Noise Generators...................................................................235
4.8.3 Equivalent Input Noise Current.........................................236
4.8.4 Pole-Zero Pattern and Dynamics........................................238
4.8.5 Responses and Noise Measurements................................242
4.8.5.1 Rise-Time and 3 dB Bandwidth...........................242
4.8.5.2 Noise Measurement and Suppression................244
4.8.5.3 Requirement for Quantum Limit.......................245
4.8.5.4 Excess Noise Cancellation Technique................246
4.8.5.5 Excess Noise Measurement.................................247
4.8.6 Remarks..................................................................................248
4.8.7 Noise Equations....................................................................249
References......................................................................................................252
5 Optical Phase Locking...............................................................................255
5.1 Overview of Optical Phase Lock Loop...........................................255
5.2 Optical Coherent Detection and Optical PLL................................258
5.2.1 General PLL Theory.............................................................258
5.2.1.1 Phase Detector.......................................................259
5.2.1.2 Loop Filter..............................................................260
5.2.1.3 Voltage-Controlled Oscillator.............................. 261
5.2.1.4 A Second-Order PLL............................................. 261
5.2.2 PLL..........................................................................................263
5.2.3 OPLL.......................................................................................265
5.2.3.1 Functional Requirements.....................................265

x Contents
5.2.3.2 Nonfunctional Requirements..............................265
5.2.4 Digital LPF Design................................................................266
5.2.4.1 Fixed-Point Arithmetic.........................................266
5.2.4.2 Digital Filter...........................................................268
5.2.4.3 Interface Board.......................................................270
5.2.4.4 FPGA Implementation..........................................272
5.2.4.5 Indication of Locking State..................................272
5.2.4.6 OPLL Hardware Details.......................................273
5.3 Performances: Simulation and Experiments.................................. 274
5.3.1 Simulation.............................................................................. 274
5.3.2 Experiment: Digital Feedback Control..............................275
5.3.2.1 Noise Sources.........................................................278
5.3.2.2 Quality of Locking State......................................278
5.3.2.3 Limitations.............................................................280
5.3.3 Simulation and Experiment Test Bed: Analog
Feedback Control..................................................................281
5.3.3.1 Simulation: Analog Feedback Control Loop......281
5.3.3.2 Laser Beating Experiments..................................288
5.3.3.3 Loop Filter Design.................................................289
5.3.3.4 Closed-Loop Locking of LO and Signal
Carrier: Closed-Loop OPLL.................................290
5.3.3.5 Monitoring of Beat Signals.................................. 291
5.3.3.6 High-Resolution Optical Spectrum Analysis......293
5.3.3.7 Phase Error and LPF Time Constant..................293
5.3.3.8 Remarks..................................................................295
5.4 OPLL for Superchannel Coherent Receiver....................................296
References......................................................................................................299
6 Digital Signal Processing Algorithms and Systems Performance.....301
6.1 Introduction........................................................................................301
6.2 General Algorithms for Optical Communications Systems........304
6.2.1 Linear Equalization..............................................................305
6.2.1.1 Basic Assumptions................................................306
6.2.1.2 Zero-Forcing Linear Equalization (ZF-LE)........307
6.2.1.3 ZF-LE for Fiber as a Transmission Channel......308
6.2.1.4 Feedback Transversal Filter................................. 310
6.2.1.5 Tolerance of Additive Gaussian Noises............. 310
6.2.1.6 Equalization with Minimizing MSE in
Equalized Signals.................................................. 312
6.2.1.7 Constant Modulus Algorithm for Blind
Equalization and Carrier Phase Recovery......... 314
6.2.2 Nonlinear Equalizer or DFEs.............................................. 319
6.2.2.1 DD Cancellation of ISI.......................................... 319
6.2.2.2 Zero-Forcing Nonlinear Equalization................ 321

xiContents
6.2.2.3 Linear and Nonlinear Equalization of a
Factorized Channel Response.............................323
6.2.2.4 Equalization with Minimizing MSE in
Equalized Signals.................................................. 324
6.3 MLSD and Viterbi.............................................................................. 324
6.3.1 Nonlinear MLSE...................................................................325
6.3.2 Trellis Structure and Viterbi Algorithm............................326
6.3.2.1 Trellis Structure.....................................................326
6.3.2.2 Viterbi Algorithm..................................................327
6.3.3 Optical Fiber as a Finite State Machine.............................328
6.3.4 Construction of State Trellis Structure..............................328
6.3.5 Shared Equalization between Transmitter and
Receivers.................................................................................329
6.3.5.1 Equalizers at the Transmitter..............................329
6.3.5.2 Shared Equalization..............................................332
6.4 Maximum a Posteriori Technique for Phase Estimation..............333
6.4.1 Method...................................................................................333
6.4.2 Estimates................................................................................334
6.5 Carrier Phase Estimation..................................................................339
6.5.1 Remarks..................................................................................339
6.5.2 Correction of Phase Noise and Nonlinear Effects...........340
6.5.3 Forward Phase Estimation QPSK Optical Coherent
Receivers.................................................................................341
6.5.4 CR in Polarization Division Multiplexed Receivers:
A Case Study.........................................................................342
6.5.4.1 FO Oscillations and Q-Penalties.........................343
6.5.4.2 Algorithm and Demonstration of Carrier
Phase Recovery......................................................345
6.6 Systems Performance of MLSE Equalizer–MSK Optical
Transmission Systems.......................................................................348
6.6.1 MLSE Equalizer for Optical MSK Systems.......................348
6.6.1.1 Configuration of MLSE Equalizer in Optical
Frequency Discrimination Receiver...................348
6.6.1.2 MLSE Equalizer with Viterbi Algorithm...........349
6.6.1.3 MLSE Equalizer with Reduced-State
Template Matching...............................................351
6.6.2 MLSE Scheme Performance................................................351
6.6.2.1 Performance of MLSE Schemes in 40 Gb/s
Transmission Systems...........................................351
6.6.2.2 Transmission of 10 Gb/s Optical
MSK Signals over 1472 km
SSMF Uncompensated Optical Link..................352
6.6.2.3 Performance Limits of Viterbi–MLSE
Equalizers...............................................................355
6.6.2.4 Viterbi–MLSE Equalizers for PMD Mitigation....359

xii Contents
6.6.2.5 On the Uncertainty and Transmission
Limitation of Equalization Process.....................364
References......................................................................................................365
7 DSP-Based Coherent Optical Transmission Systems..........................369
7.1 Introduction........................................................................................369
7.2 QPSK Systems.....................................................................................371
7.2.1 Carrier Phase Recovery........................................................371
7.2.2 112 G QPSK Coherent Transmission Systems...................371
7.2.3 I–Q Imbalance Estimation Results..................................... 374
7.2.4 Skew Estimation....................................................................375
7.2.5 Fractionally Spaced Equalization of CD and PMD..........377
7.2.6 Linear and Nonlinear Equalization and Back-
Propagation Compensation of Linear and
Nonlinear Phase Distortion................................................377
7.3 16 QAM Systems.................................................................................381
7.4 Tera-Bits/s Superchannel Transmission Systems..........................385
7.4.1 Overview................................................................................385
7.4.2 Nyquist Pulse and Spectra..................................................386
7.4.3 Superchannel System Requirements.................................388
7.4.4 System Structure...................................................................389
7.4.4.1 DSP-Based Coherent Receiver.............................389
7.4.4.2 Optical Fourier Transform-Based Structure.....394
7.4.4.3 Processing...............................................................395
7.4.5 Timing Recovery in Nyquist QAM Channel....................398
7.4.6 128 Gb/s 16 QAM Superchannel Transmission................399
7.4.7 450 Gb/s 32 QAM Nyquist Transmission Systems...........401
7.4.8 DSP-Based Heterodyne Coherent Reception Systems......403
References......................................................................................................407
8 Higher-Order Spectrum Coherent Receivers........................................409
8.1 Bispectrum Optical Receivers and Nonlinear Photonic Pre-
Processing...........................................................................................409
8.1.1 Introductory Remarks..........................................................409
8.1.2 Bispectrum............................................................................. 411
8.1.3 Bispectrum Coherent Optical Receiver............................. 412
8.1.4 Triple Correlation and Bispectra......................................... 412
8.1.4.1 Definition................................................................ 412
8.1.4.2 Gaussian Noise Rejection..................................... 413
8.1.4.3 Encoding of Phase Information.......................... 413
8.1.4.4 Eliminating Gaussian Noise................................ 413
8.1.5 Transmission and Detection................................................ 414
8.1.5.1 Optical Transmission Route and Simulation
Platform.................................................................. 414

xiiiContents
8.1.5.2 Four-Wave Mixing and Bispectrum
Receiving............................................................. 415
8.1.5.3 Performance........................................................... 415
8.2 NL Photonic Signal Processing Using Higher-Order Spectra......419
8.2.1 Introductory Remarks.......................................................... 419
8.2.2 FWM and Photonic Processing...........................................420
8.2.2.1 Bispectral Optical Structures..............................420
8.2.2.2 The Phenomena of FWM.....................................422
8.2.3 Third-Order Nonlinearity and Parametric
FWM Process.........................................................................424
8.2.3.1 NL Wave Equation................................................424
8.2.3.2 FWM Coupled-Wave Equations..........................425
8.2.3.3 Phase Matching.....................................................427
8.2.3.4 Coupled Equations and Conversion
Efficiency.............................................................. 427
8.2.4 Optical Domain Implementation.......................................428
8.2.4.1 NL Wave Guide.....................................................428
8.2.4.2 Third-Harmonic Conversion...............................429
8.2.4.3 Conservation of Momentum...............................429
8.2.4.4 Estimate of Optical Power Required for
FWM.....................................................................429
8.2.5 Transmission Models and NL Guided Wave Devices......430
8.2.6 System Applications of Third-Order Parametric
Nonlinearity in Optical Signal Processing.......................431
8.2.6.1 Parametric Amplifiers..........................................431
8.2.6.2 Wavelength Conversion and NL Phase
Conjugation............................................................436
8.2.6.3 High-Speed Optical Switching...........................437
8.2.6.4 Triple Correlation..................................................442
8.2.6.5 Remarks..................................................................448
8.2.7 NL Photonic Pre-Processing in Coherent Reception
Systems...................................................................................449
8.2.8 Remarks..................................................................................455
References......................................................................................................456
Index......................................................................................................................459

xv
Preface
Optical communication technology has been extensively developed over the
last 50 years, since the proposed idea by Kao and Hockham [1]. However, only
during the last 15 years have the concepts of communication foundation, that
is, the modulation and demodulation techniques, been applied. This is pos-
sible due to processing signals using real and imaginary components in the
baseband in the digital domain. The baseband signals can be recovered from
the optical passband region using polarization and phase diversity tech-
niques, as well as technology that was developed in the mid-1980s.
The principal thrust in the current technique and technology differs dis-
tinctively in the processing of baseband signals in the discrete/sampled digi-
tal domain with the aid of ultra-high-speed digital signal processors and
analog-to-digital and digital-to-analog converters. Hence, algorithms are
required for such digital processing systems.
Over the years, we have also witnessed intensive development of digital
signal processing algorithms for receivers in wireless transceivers, and espe-
cially in band-limited transmission lines to support high-speed data com-
munications [2] for the Internet in its early development phase.
We have now witnessed applications and further development of the algo-
rithms from wireless and digital modems to signal processing in lightwave
coherent systems and networks. This book is written to introduce this new
and important development direction of optical communication technology.
Currently, many research groups and equipment manufacturers are attempt-
ing to produce real-time processors for practical deployment of these DSP-
based coherent transmission systems. Thus, in the near future, there will be
new and significant expansion of this technology due to demands for more
effective and memory-efficient algorithms in real time. Therefore, the author
believes that there will be new books addressing these coming techniques
and technological developments.
This book is organized into seven chapters. Chapter 1 gives an introduc-
tion and overview of the development of lightwave communication tech-
niques from intensity modulation direct detection, to coherent modulation
and detection in the early stage (1980s), to self-homodyne coherent in the last
decade of the 20th century, and then current digital signal processing tech-
niques in coherent homodyne reception systems for long-haul nondispersion
compensating multispan optical links. Thus, a view of the fiber transmission
property is given in Chapter 2. Chapter 3 then discusses the optical modula-
tion technique using external modulators, especially the modulation of the
inphase and quadrature phase components of the quadrature amplitude
modulation scheme.

xvi Preface
Chapters 4 and 5 then introduce optical coherent reception techniques
and technological development in association with digital signal proces-
sors. Optical phase locking of the local oscillator and the channel carrier is
also important for performance improvement of reception sensitivity, and is
described in Chapter 5.
Chapters 6 and 7 present digital processing algorithms and their related
performances of some important transmission systems, especially those
employing quadrature modulation schemes, which are considered to be the
most effective ones for noncompensating fiber multispan links.
Further, the author would like to point out that the classical term “syn-
chronization systems” employed some decades ago can now be used in its
true sense to refer to DSP-based coherent reception transmission systems.
Synchronization refers to processing at the receiver side of a communica-
tions systems link, in order to recover optimal sampling times and compen-
sate for frequency and phase offsets of the mixing of the modulated channel
and local oscillator carriers, induced by the physical layers and transmission
medium. In digital optical communications, designs of synchronization algo-
rithms are quite challenging due to their ultrahigh symbol rates, ultrahigh
sampling rates, minimal memory storage and power consumptions, strin-
gent latency constraints, and hardware deficiencies. These difficulties are
coupled with the impairments induced by other nonlinear physical effects
in the linearly polarized guided modes of the single-mode fibers, when more
wavelength channels are multiplexed to increase transmission capacity.
Recently, there have been published works on synchronization algorithms
for the digital coherent optical communications systems, with some of these
aspects touched upon in this book, but still, little is known about the optimal
functionality and design of these DSP-based algorithms due to impacts of
synchronization error. We thus expect extensive research on these aspects
in the near future.
Finally, higher-order spectra techniques, a multidimensional spectrum
of signals with amplitude and phase distribution for processing in optical
coherent receivers, are introduced.
The author wishes to thank his colleagues at Huawei Technologies Co.
Ltd. for discussions and exchanges of processing techniques in analytical
and experimental works during the time that he worked in several fruit-
ful projects of advanced optical transmission systems. He also acknowl-
edges the initial development phases of major research projects funded by
the Australian Industry RD Grant, involving development of DSP-based
algorithms with colleagues of CSIRO Australia and Ausanda Pty. Ltd. of
Melbourne, Australia. A number of his former PhD and undergraduate stu-
dents of Monash University of Melbourne, Australia have also contributed
to discussions and learning about processing algorithms for the minimum
shift keying self-heterodyne reception.
Last but not least, the author thanks his family for their understanding
during the time that he spent compiling the chapters of the book. He also

xviiPreface
thanks Ashley Gasque of CRC Press for her encouragement during the time
of writing each chapter of this book.
Le Nguyen Binh
Huawei Technologies, European Research Center
Munich, Germany
References
1. K.C. Kao and G.A. Hockham, Dielectric-fibre surface waveguides for optical
frequencies, Proc. IEE, 113(7), 1151–1158, 1966.
2. A.P. Clark, Equalizers for Digital Modems, Pentech Press, London, 1985.
MATLAB® and Simulink® are registered trademarks of The MathWorks, Inc.
For product information, please contact:
The MathWorks, Inc.
3 Apple Hill Drive
Natick, MA 01760-2098 USA
Tel: 508 647 7000
Fax: 508-647-7001
E-mail: info@mathworks.com
Web: www.mathworks.com

xix
Author
Le Nguyen Binh earned his BE(Hons) and
PhD degrees in electronic engineering and
integrated photonics in 1975 and 1978, respec-
tively, both from the University of Western
Australia, Nedlands, Western Australia. In
1980, he joined the Department of Electrical
Engineering of Monash University after
spending 3 years as a research scientist with
CSIRO Australia.
Dr. Binh has worked on several major advanced world-class projects, espe-
cially the Multi-Tb/s and 100G-400G DWDM optical transmission systems
and transport networks, employing both direct and coherent detection tech-
niques. He has worked for the Department of Optical Communications of
Siemens AG Central Research Laboratories in Munich, Germany, and the
Advanced Technology Centre of Nortel Networks in Harlow, England.
He was the Tan-Chin Tuan Professorial Fellow of Nanyang Technological
University of Singapore. He was also a professorial fellow at the Faculty of
Engineering of Christian Albretchs University in Kiel, Germany.
Dr. Binh has authored and coauthored more than 250 papers in leading
journals and refereed conferences, and 7 books in the field of photonics
and digital optical communications. His current research interests are in
advanced modulation formats for superchannel long-haul optical transmis-
sion, electronic equalization techniques for optical transmission systems,
ultrashort pulse lasers and photonic signal processing, optical transmission
systems, and network engineering.
Dr. Binh has developed and taught several courses in engineering, such
as Fundamentals of Electrical Engineering, Physical Electronics, Small-
Signal Electronics, Large-Signal Electronics, Signals and Systems, Signal
Processing, Digital Systems, Micro-Computer Systems, Electromagnetism,
Wireless and Guided Wave Electromagnetics, Communications Theory,
Coding and Communications, Optical Communications, Advanced Optical
Fiber Communications, Advanced Photonics, Integrated Photonics, and Fiber
Optics. He has also led several courses and curriculum development in elec-
trical and electronic engineering (EEE), and joint courses in physics and EEE.
In January 2011, he joined the European Research Center of Huawei Co.
Ltd., working on several engineering aspects of 100G, Tb/s long-haul, and
metro-coherent optical transmission networks. He is also the series editor
for Optics and Photonics for CRC Press and chairs Commission D (Electronics
and Photonics) of the National Committee of Radio Sciences of the Australian
Academy of Sciences.

xxi
Abbreviations
4QAM equivalent with QPSK
16QAM QAM with 16 point constellation
ADC analog-to-digital conversion/converter
Algo algorithms
αNL scaling factor of nonlinear phase noises (NLPN)
ASE amplification stimulated emission
ASK amplitude shift keying
Balanced detectors BalD
BalORx balanced optical receiver
BP back propagation
CD chromatic dispersion
CMA constant modulus amplitude
Co-OFDM coherent optical orthogonal frequency division
multiplexing
Co-ORx coherent optical receiver
CoQPSK coherent QPSK
D(λ) waveguide dispersion factor
DAC digital-to-analog conversion/converter
DCF dispersion compensating fiber
DD direct detection
DFE decision feedback equalizer
DQPSK differential QPSK
DTIA differential transimpedance amplifier
DuoB duobinary
DWDM dense wavelength division multiplexing
ECL external cavity laser
EDFA erbium-doped fiber amplifier/amplification
ENOB effective number of bits of ADC or DAC
EQ equalization
ESA electrical spectrum analyzer
ETDM electrical time division multiplexing
FC fiber coupler
FDEQ frequency domain equalization
FF feedforward
FFE feedforward equalizer
FIR finite inpulse response
FMF few mode fiber
FSK frequency shift keying

xxii Abbreviations
FTVF feedback transversal filter
FWM four-wave mixing
Ga/s Giga samples per second
GB or GBaud Giga-baud or giga symbols/s
Gb/s Giga-bits per second
GBaud Giga symbols/s—see also Gsy/s
GSa/s Giga samples per seconds
GSy/s Giga symbols per second, i.e., Giga bauds
HD hard decision
IM intensity modulation
IM/DD intensity modulation/direct detection
IQ inphase quadrature
ISI intersymbol interference
iTLA integrated tunable laser assembler
IXPM intrachannel cross-phase modulation
LD laser diode
LE linear equalizer
LMS least-mean-square
LO local oscillator
LPF low-pass filter
LSB least significant bit
LUT look-up table
M(λ) material dispersion factor
MAP maximum a posteriori probability
M-ary QAM M-order QAM, M = 4, 8, 166, 32,...,256,...
MIMO multiple input/multiple output
MLD multilane distribution
MLSE minimum likelihood sequence estimation/estimator
MLSE maximum likelihood sequence estimation
MMF multimode fiber
MSB most significant bit
MSE mean square error
MSK minimum shift keying
MZDI Mach–Zehnder delay interferometer
MZIM Mach–Zehnder interferometric/intensity modulator
MZM Mach–Zender modulator
NL nonlinear
NLE nonlinear equalizer
NLPE nonlinear performance enhancement
NLPN nonlinear phase noise
NLSE nonlinear Schrödinger equation
NRZ nonreturn to zero
Nyquist QPSK Nyquist pulse-shaping modulation QPSK
NZDSF nonzero dispersion-shifted fiber
OA optical amplifier

xxiiiAbbreviations
OFDM orthogonal frequency division multiplexing
OFE optical front-end
OOK on-off keying
OPLL optical phase lock loop
ORx optical receiver
OSA optical spectrum analyzer
OSNR optical signal-to-noise ratio
OTDM optical time domain multiplexing
PAM pulse amplitude modulation
PD photodetector
PDF probability density function
PDL polarization-dependent loss
PDM polarization division multiplexing
PDM-QAM polarization multiplexed QAM
PDM-QPSK polarization multiplexed QPSK
PDP photo-detector pair—see also balanced detection
pi/2 HC pi/2 hybrid coupler—optical domain
PLL phase-locked loop
PMD polarization mode dispersion
PMF polarization-maintaining fiber
PSK phase shift keying
QAM quadrature amplitude modulation
QPSK quadrature phase shift keying
RF radio frequency
RFS recirculating frequency shifting
RFSCG RFS comb generator
RIN relative intensity noise
ROA Raman optical amplification
Rx receiver
RZ return-to-zero
RZ33, RZ50, RZ63 RZ pulse shaping with full-width half mark of the
“1” pulse equal to 33%, 50%, and 63% of the pulse
period, respectively
SMF single-mode fiber
SoftD soft decision
SOP state of polarization
SPM self-phase modulation
SSFM split-step Fourier method
SSMF standard single-mode fiber (G.652)
TDEQ time domain equalization
TDM time division multiplexing
TF transfer function
TIA transimpedance amplifier
TIA gain transimpedance gain, ZT
TVE transversal equalizer

xxiv Abbreviations
TVF transversal filter
Tx transmitter
VOA variable optical attenuator
VSTF Volterra series transfer function
XPM cross-phase modulation

1
1
Overview of Optical Fiber Communications
and DSP-Based Transmission Systems
1.1 Introduction
Since the proposed “dielectric waveguides” in 1966 by Charles Kao and
George Hockham of Standard Telephone Cables (STC) Ltd. in Harlow of
England [1], optical fiber communication systems have used lightwaves as
carriers to transmit information from one place to the other. The distance of a
few meters in laboratory, to a few kilometers, to hundreds of kilometers, and
now thousands of kilometers in the first decade of this century with bit rates
reaching from few tens of Mb/s in late 1960s to 100 Gb/s and Tb/s at present.
Tremendous progress has been made though nearly the last 50 years due to
two main significant phenomena, the guiding of lightwaves in optical fibers
and transmission, and modulation and detection techniques. The progress
of long-haul transmission with extremely high capacity is depicted in Figure
1.1, with transmission distance reaching several thousands of kilometers of
one SMF (single mode fiber). We can see since the invention of optical ampli-
fiers, the Erbium doped fiber amplifier (EDFA), in the late 1980s, the dem-
onstration in experimental platform has reached 2.5 Gb/s, that is when the
attenuation of the transmission medium can be overcome and only the dis-
persion remains to be resolved, hence the dispersion management technique
developed to push the bit rate to 10 Gb/s. Thence the transmission capacity
is further increased with multiplexing of several wavelength channels in the
C-band as well as L- and S- bands. With gain equalization, the total capacity
was able to reach 40–100 Gbps in 1995. The exploitation of spectral efficiency
would then be exploded with further RD and experimental demonstration
by deploying channels over the entire C-band and then over L- and S-bands
using hybrid amplifiers to reach 2000 Gb/s at the turn of this century. So over
the first decade of this century we have witnessed further progresses to push
the capacity with high spectral efficiency, coherent detection, and digital sig-
nal processing (DSP) techniques employed at both the transmitter and receiv-
ers to achieve 64 Tbps and even higher in the near future. Coherent detection
allows further gain in the receiver sensitivity and DSP, overcoming several

2 Digital Processing
difficulties in coherent receiving and recovery of signals. Furthermore, the
modulation techniques such as QPSK, M-ary QAM, and spectral shaping
such as Nyquist and orthogonality have assisted in the packing of high sym-
bol rates in the spectrum whose bandwidth would be the same as that of
the symbol rate of the transmitted channels. DSP algorithms have also been
employed to tackle problems of dispersion compensation, clock recovery,
compensation on nonlinear effects, polarization dispersion, and cycle slip in
walk-off over transmission. It is noted that the transmission is a multi-span
optically amplified line and no dispersion compensation is used, unlike the
dispersion-managed transmission systems developed and deployed in sev-
eral terrestrial and undersea networks currently installed, as depicted in
Figures 1.2 and 1.3.
This chapter is thus organized as follows: the next section gives an over-
view of the fiber development over the last few decades and the important
features of the single- or even few-mode fibers currently attracting much
interest for increasing the transmission capacity. Section 1.3 then gives an
overview of advanced modulation techniques, and Section 1.4 gives an over-
view of coherent detection and DSP process. Details of DSP algorithms will
be discussed briefly, then later chapters will provide more details, along with
a description of improvement of transmission performance.
This introduction chapter is organized in the following sequence: The his-
torical aspects of optical guiding and transmission techniques over the last
50 years are outlined, followed by an introduction of present progress in the
processing of received signals as well as a brief explanation of the generation
of modulated signals in the digital domain.
105
104
103
102
101
100
10
Dispersion
management2.5
Optical amp
40
OA gain equ
320, 640
FEC
6 Tbps
hybrid OA
(EDFA + ROA)
10 Tbps
coherent–DSP
64 Tbps
coherent–DSP
FEC
Bitrate(Gbps)
Year
1988 1990 1995 2000 2005 2010 2015
FIGURE 1.1
Experimentally demonstrated single-mode, single-fiber transmission capacity.

3Overview
1.2 From Few Mb/s to Tb/s: Transmission and Receiving
for Optical Communications Systems
1.2.1 Guiding Lightwaves over the Last 40 Years
Since the proposed dielectric waveguides, the idea of transmission via an
optical waveguide was like a lightening stroke through the telecommunica-
tion engineering, physics, and material engineering communities, alike. The
physicists, mathematicians, and electrical engineers were concerned with
the design of the optical waveguides, the guiding conditions, and the forma-
tion of the wave equations employed Maxwell’s equations and their solutions
for guiding and propagation, as well as the eigenvalue equations subject to
the boundary conditions, among others. Material engineers played a very
important role in determining the combination of elements of the guided
medium so that the scattering loss was minimal and, even more important,
that the fabrication of such optical waveguides and hence the demonstration
of the guided waves through such waveguides.
In 1970, the propagation and fabrication of circular optical waveguides were
then successfully demonstrated with only 16 dB/km at red line of 633 nm
wavelength, thus the name optical fibers, which consist of a circular core and
cladding layer. Don Keck’s research alongside two other Corning scientists,
FIGURE 1.2
Global submarine cable systems.

Maurer and Schultz, transformed the communications industry to the fore-
front of the communications revolution, from narrow bandwidth with elec-
tromagnetic radiation to guiding lightwaves. Compared to the attenuation of
0.2 dB/km today, that attenuation factor was not ideal, but it did serve as a piv-
otal point in time for the current revolution of global information systems [2,3].
However, the employment of guided lightwaves in transmission for com-
munication purposes has evolved over the last four decades from multimode
to single mode, and then once again in the first decade of this century when
the few mode fibers attracted once again the “multimode” used in transmis-
sion to increase the total capacity per fiber. The detection of lightwaves also
evolves from direct to coherent, then direct self-homodyne, and then coher-
ent homodyne with analog-to-digital processing. The structure of transmis-
sion systems over the decades is depicted in Figure 1.4, which shows the
evolution of such system through the end of the twentieth century when
FIGURE 1.3
Optical fiber cable networks in Southeast Asia and the Australia Oceana Region.

5Overview
direct detection, in fact self-homodyne detection, with external modulation
of the lightwaves emitted from an external cavity laser whose line width is
sufficiently narrow and various modulation formats employed to exploit the
combat of dispersion and sensitivities of the optical receivers.
The transmission systems were limited due to attenuation or losses of the
fibers and associated components as well as the receiver sensitivity. The
transmission was at first operating in the 810 nm near the infrared region
due to availability of the source developed in GaAs. This wavelength is then
shifted to 1310 nm where the dispersion of the fiber is almost zero, thus lim-
ited only by the attenuation factor. This loss can be further reduced when
the wavelength is moved to 1550 nm at which the Rayleigh scattering for
silica-based fiber is lowest with a value of 0.2 dB/km. This is about half of the
attenuation factor at 1310 nm spectral region. However, at this wavelength
the dispersion is not zero. The attenuation was further eliminated by the
invention of optical amplification by erbium-doped fiber amplifiers.
External
cavity lasers
(ECL)
PDM-IQ
optical mod.
DAC
Prog.
sequence
Local
oscillator
(ECL)
Opt. hybrid
coupler
4 × optical bal. Rx
Ultra-high
sampling rate
ADC
Digital
signal
processing
Non-DCF SSMF dispersive optically
amplified transmission lines
ultra-long haul
Booster opt
amp
IM optical Tx
at 1550 nm
FP and DFB
lasers
DD optical receiver
(P-i-n or APD)
at 1550 nm
Single mode
fibers
(a)
O/E repeater
DD ORx
+
Tx
Single mode
fibers
O/E repeater
DD ORx
+
Tx
(b)
Repeater
distance ~
40 km
Span
distance ~ 80–
100 km
FIGURE 1.4
Schematic structures of the first and recent single-mode optical transmission systems:
(a) single-mode non-DCF optically amplified transmission system with DSP-based coherent
detection, the fiber can be a single-mode or few-mode type; (b) nonoptically amplified repeated
link; (b) optically repeated transmission line with coherent reception. Note the optical trans-
mission line is non-DCF (dispersive) and hence a dispersive optically amplified link.

Optical amplification has changed design considerations for long-haul trans-
mission. With 30 dB gain in the optical domain the fiber attenuation becomes
negligible, and over 100 km or 80 km can be equalized without much difficulty
as far as the power to the optical channels can satisfy the amplification min-
imum input level. Furthermore, the insertion loss of integrated modulators
would pose no obstacle for their uses as external modulators, which would
preserve the linewidth of the laser and hence further reduce the dispersion
effects and then the pulse broadening. The schematic structure of this optically
amplified transmission system is shown in Figure 1.5e. Note also that distrib-
uted optical amplification such as Raman amplifiers are also commonly used
in transmission link, in which the distance between spans is longer than the
maximum optical gain provided by EDFA. Such requirement would normally
be faced by the designer in an overseas environment. For example, the optical
link between Melbourne Australia and Hobart of Tasmania, the large island
in the southern-most location of Australia. The coast-to-coast link distance is
about 250 km, and thus the EDFA is employed as a power booster and optical
pre-amplification of the receiver, and Raman pumping from both sides (i.e.,
co- and contra pumping with respect to the signal propagation direction) of
the link located on shore to provide a further 30 dB gain.
During the last decade of the twentieth century we witnessed an explosion
of research interests in pushing the bit rates and transmission distance with
the dispersion of the standard optical fibers compensated by dispersion com-
pensating fiber; that is, management of the dispersion of the transmission link
either by DCF or by distributed dispersion optical compensators such as fiber
Bragg gratings (FBG). However, the detection was still by direct detection, or
by self-homodyne detection and the processing was still in analog domain.
Another way of compensating the dispersion of the fiber link can be by
pre-distortion or chirping the phase of the lightwave source at the trans-
mitter. The best technique is to use the digital-to-analog conversion (DAC)
and to tailor the phase distortion of the lightwaves. This is done by modu-
lating the optical modulator by the analog outputs of the DAC, which can
be programmable and provide the flexibility that the sampling rate of DAC
can meet the Nyquist criteria. This can be met due to significant progresses
in the development of digital signal processors for wireless communication
systems and computing systems. Under such digital processing, the optical
signals can be pre-distorted to partially compensate the dispersion as well as
post compensation at the receiver DSP sub-systems.
The DSP field could then be combined with the opto-electronic detection
to advance the technology for optical communication systems.
Coherent detection has then been employed with DSP to overcome several
hurdles that were met by the development and research of coherent communi-
cations in the early 1980s, when single-mode fibers were employed. The limited
availability of narrow linewidth sources that would meet the requirement for
receiver sensitivities by modulation formats such as DPSK (differential phase
shiftkeying),DQPSK,FSK,MSK,andtherecoveryofclockforsampling,among

7Overview
others, can be resolved without much difficulty if ultra-high-speed analog-to-
digital converter (ADC) is available and combined with ultra-high-speed DSP.
Thus, we have witnessed once again significant progress in the DSP of
advanced modulated lightwaves and detection for ultra-long-haul, ultra-
sensitive optical fiber communications, without the management of disper-
sion. A generic schematic of the most advanced transmission is shown in
Figure 1.4b, in which both DAC and ADC at the transmitter receive analog
IM optical Tx
at 810 nm FP
laser
DD optical receiver
(P-i-n or APD)
at 810 nm
Multimode
fibers
IM optical Tx
at 1310 nm
FP laser
DD ORx
(P-i-n or APD)
at 1310 nm
Multimode and single
fibers
IM optical Tx
at 1550 nm
FP and DFB
lasers
DD optical receiver
(P-i-n or APD)
at 1550 nm
Single mode
fibers
IM optical Tx
at 1550 nm DFB
lasers + external
cavity
and external
modulator
DD optical receiver
(P-i-n or APD)
at 1550 nm
Single mode
fibers
Local
oscillator
Polarization and
phase diversity
IQ modulation
optical Tx
at 1550 nm ECL
(external cavity lasers)
DD optical receiver
(P-i-n or APD)
at 1550 nm
Single mode fiber span + optical amps
+
DCF (dispersion compensation fibers)
Advanced modulation formats
EDFAs
EDFAs
(a)
(b)
(c)
(d)
(e)
Raman pump
Coherent receiver
FIGURE 1.5
Schematic structures of optical transmission systems over the decades: (a) earliest multimode
systems, (b) single-mode fiber transmission, (c) single-mode fiber as the transmission medium
with 1550 nm wavelength, (d) first optical coherent systems with external modulator and cav-
ity lasers and homodyne or heterodyne with polarization and phase diversity detection in
analog domain, and (e) optically amplified single-mode fiber links with lumped EDFA and
distributed Raman amplification.

signals produced from conventional coherent optical receivers. In contrast to
the coherent and DSP-based optical transmission, Figure 1.4a shows the first
single-mode optical fiber transmission system with several opto-electronic
repeaters, where the distance between them is about 40 km, deployed in
the 1980s. In these systems the data sequence must be recovered back into
the electrical domain, which is then used to modulate the lasers for further
transmission. The distance between these repeaters is about 40 km for a
wavelength of 1550 nm. It is at this distance that several housing infrastruc-
tures were built and remain to be the housing for present-day optical repeat-
ers, hence the span length of 80 km, with optical attenuation at about 22 dB
that fits well into the optical amplification using lumped amplifiers such as
the EDFAs for the C-band region of 1550 nm.
1.2.2 Guiding Lightwaves: Single Mode, Multimode, and Few Mode
Lightwaves are coupled into the circular dielectric waveguide, the optical
fiber whose refractive index profile consists of a core region and a circular
covering on the outside. The refractive index difference between the core and
the cladding regions would normally be very small, in order of less than 1%,
0.3% typically. The main principles of operation of such guiding lightwaves
are due to the condition that would satisfy the boundary conditions and the
guiding such that the interface between the core and cladding would not
contribute much to the scattering of the guided waves. Thus, typically the
dimension for standard single-mode optical fiber (SSMF) is a core diameter
~8.0 μm, with a cladding of about 125 μm to assure mechanical strength and
distribution of the tails of the guided waves in the core. The refractive index
is about ~0.3% and a mode spot size of about 4.2 μm. The operational param-
eters of the SSMF are a dispersion factor of 17 ps/nm km at 1550 nm with
a dispersion slope of 0.01 ps/μm2, and a nonlinear coefficient of 2.3 × 10−23
μm−2 with GeO2:doped silica as the core materials. The cutoff wavelength of
the SSMF is in the 1270–1290 nm range, above which only one single mode,
the fundamental mode LP01, can be guided. This linearly polarized mode
consists of two polarized modes, the EH11 and HE11, or the field distribution
is nearly the same but the polarizations of these modes are spatially orthogo-
nal. Under the nonuniformity of the core of the fiber, these two polarized
modes travel at different propagation velocity due to the difference in their
propagation constant and hence the delay difference. This delay difference is
termed as the polarization mode dispersion.
1.2.3 Modulation Formats: Intensity to Phase Modulation,
Direct to External Modulation
The invention and availability of optical amplification in the 1550 nm with
EDF has allowed integrated community reconsideration of the employment
of integrated optical modulators, especially the LiNbO3-based components

9Overview
due to reasonably high insertion loss, about 3–4 dB for a single Mach–Zehnder
interferometric modulator (MZIM). The MZIM offers significant features in
terms of bandwidth and extinction ration, defined as the difference in inten-
sity, or field between the “on” and “off.” The bandwidth of LiNbO3 can be up
to 50 GHz if the travelling wave electrode can be fabricated with the thick-
ness sufficiently high.
Thus we have seen in recent years several modulation formats, especially
the quadrature amplitude modulation (QAM) techniques in which both the
real and imaginary or inphase and quadrature components are used to con-
struct the constellation in the complex plane, as shown in Figure 1.6 for M = 2,
4, 8, and 16. The phase shift keying modulation formats were employed in the
first-generation optical communications in guided wave systems in the 1980s.
1.2.4 Coherent and Incoherent Receiving Techniques
Coherent, incoherent, or direct reception of the modulated and transmitted
lightwave modulated signals are currently considered, but depending on
2(a) (b)
(c) (d)
1
0
–1
–2
–2 –1 0
Inphase (a.u.)
Inphase
Quadrature
Inphase (a.u.)
1 2
2
1
0
–1
–2
–2 –1 0 1 2
2
1
0
–1
–2
–2 –1 0 1 2
2
1
0
–1
–2
–2 –1 0 1 2
FIGURE 1.6
Constellation of M-ary QAM with M = 2 (a), 4 (b), 8 (c), and 16 (d).

applications and whether they are in the long haul (carrier side), or metro-
politan access (client side, or access networks). Direct modulation should also
be considered as this solution for offering significantly inexpensive deploy-
ment in metro networks, while coherent solution would offer significant
advantages to long-haul transmission systems in terms of reach and symbol
rates or baud rates. Both incoherent and coherent systems can employ digital
processing techniques to improve the receiver sensitivity and error coding
to achieve coding gain, thus gaining longer transmission distance. We have
witnessed the development of chirp-managed lasers by taking advantage of
the biasing of distributed feedback laser (DFB) about 4 to 5 times the level of
the laser threshold, so that the inverse NRZ driving of the DFB would pro-
duce chirp and thence the phase difference between the “1” and “0” about
π _rads. Thus, any dispersion due to these pulses over long distances of fiber
would be cancelled out, hence the dispersion tolerance of such management
of the chirp by laser direct modulation.
1.2.5 Digital Processing in Advanced Optical Communication Systems
A generic block diagram of the digital coherent receiver and associate DSP
techniques is shown in the flow chart presented in Figure 1.6. Obviously
the reception of the modulated and transmitted signals is conducted via
an optical receiver in coherent mode. Commonly known in coherent recep-
tion techniques are homodyne, heterodyne, and now intradyne, which
are dependent on the frequency difference between the local oscillator
and that of the carrier of the received channel. For homodyne-coherent
detection, the frequency difference is nil, thus locking the local oscillator
frequency to that of the carrier of the channel is essential, while with het-
erodyne coherent detection there is a frequency difference that is outside
the 3 dB bandwidth of the channel. When the frequency difference is less
than the 3 dB and can be close to the carrier, then the coherent reception is
of intra-dyne type. Indeed this difference has degraded the first-generation
coherent reception systems for optical fiber communications in the mid-
1980s. With DSP, the phase carrier recovery techniques can be developed
and overcome these difficulties. Heterodyne reception would require an
electrical filter to extract the beating channel information outside the sig-
nal band and may become troublesome, with cross talks between received
channels. With the bit rate and symbol rate now expected to reach several
tens of GHz, as well as due to its complexity, heterodyne detection is not
the preferred technique.
For a DSP-based coherent receiver, the availability of a high-speed sam-
pling rate ADC is a must. However, with tremendous progress in digital tech-
nology, ADC at 56–64 GSa/s is available and the sampling speed is expected
to rise when 28 nm SiGe technologies are employed. In addition, significant
progress in the development of algorithms for processing the received sam-
pled data sequence in real time must be made, so that real-time recovery of

11Overview
data sequences can be realized. Currently, offline processing has been done to
ensure the availability of processing algorithms.
1.3 Digital Modulation Formats
1.3.1 Modulation Formats
In this book we concentrate on digital modulation formats as a way of car-
rying information over long distance via the use of the optical carrier. These
modulation formats have been developed over the last 50 years and are now
well known. However, for completeness we will provide a brief revision
of the concepts, as these will lead to further detailed understanding of the
modulation of the lightwaves in the optical domain.
The modulation of the lightwave carrier can be in the following forms:
The optical signal filed has the ideal form during the duration of one bit
period, given as

E t E t a t t t t t Ts P( ) ( ) ( )cos ( ) ( )= +  ≤ ≤w q⋅ 0

(1.1)
where Es(t), EP(t), a(t), ω(t), and θ(t) are the signal optical field, the polarized
field coefficient as a function of time, the amplitude variation, the optical fre-
quency change with respect to time, and the phase variation with respect to
time, respectively. Depending on the modulation of the carrier by amplitude,
frequency, or phase, as follows:
• For amplitude shift keying (ASK), the amplitude a(t) takes the value
a(t) 0 for a “1” symbol and the value of 0 for a “0” symbol. Other val-
ues such as the angular frequency and the phase parameter remain
unchanged over one bit period.
• For phase shift keying (PSK), the phase angle θ(t) takes a value of π
rad for a “1” symbol, and zero rads for the symbol “0” so that the dis-
tance between these symbols on the phase plane is at maximum, and
hence minimum interference or error can be obtained. These values
are changed accordingly if the number of phase states is increased, as
shown in Figure 1.7. The values of a(t), ω(t), and Ep(t) remain unchanged.
• For frequency shift keying (FSK), the value of ω(t) takes the value ω 1
for the “1” symbol and ω2 for the “0” symbol. The values of a(t), θ(t),
and Ep(t) remain unchanged. Indeed, FSK is a form of phase modula-
tion provided that the phase is continuous. Sometimes continuous
phase modulation is also used as the term for FSK. In the case that
the frequency spacing between ω 1 and ω2 equals to a quarter of the
bit rate, then the FSK is called minimum shift keying.

• For polarization shift keying (PolSK), we have Ep(t) taking one direc-
tion for the “1” symbol and the other for the “0” symbol. Sometimes
continuous polarization of light waves is used to multiplex two opti-
cally modulated signal sequences to double the transmission capacity.
• Furthermore, to increase the transmission capacity there is a pos-
sibility to increase the number of bits per symbol by using M-ary
QAM, such as 16 QAM, 32 QAM, or 64 QAM, for which constella-
tions are as shown in Figures 1.8 and 1.9. However, the limitation is
that the required OSNR would be increased accordingly. For exam-
ple, an extra 6–7 dB would be required for 16 QAM as compared to
QPSK, which is a 4 QAM. The estimated theoretical BER versus SNR
is depicted in Figure 1.10 by using the bertoool.m in MATLAB®.
Clearly we can observe that at a BER of 1e–4 the required energy per bit
of 16 QAM is about 5 dB above that required for QPSK. So where can we get
this energy for a symbol in the optical domain? We can naturally increase
the carrier power to achieve this, but this will hit the threshold level of non-
linear effects, thus further penalty. This can be resolved by a number of
(c) 10
Rectangular
sinc
–10
–20
–30
–40
–50
–2 –1.5 –1 –0.5
Normalized frequency
Powerspectraldensity
0 0.5 1 1.5 2
0
0
–5
–10
–15
|H(f)|2(dB)
Powerspectrum(dB)
–20
–25
–0.4 –0.2 0
(a) (b)
f/Ra
0.2 0.4 0.6
0
–5
–10
–15
–20
–25
–0.4 –0.2 0
f/Ra
0.2 0.4 0.6
FIGURE 1.7
(a) Desired Nyquist filter for spectral equalization; (b) output spectrum of the Nyquist filtered
QPSK signal; (c) spectra of pulse sequences with sinc function and rectangular pulse shape.

13Overview
techniques that will be explained in detail in the corresponding chapters
related to transmission systems.
1.3.2 Pulse Shaping and Modulations for High Spectral Efficiency
1.3.2.1 Partial Response
The M-ary-QAM digital modulation formats form the basis of modulation
for digital optical fiber communications systems due to the availability of
(a)
(b)
(c)
“1” symbol, frequency ω1 FSK “0” symbol, frequency ω2 FSK
θ(t)
“0” symbol ASK
“0” symbol PSK
“1” symbol ASK
“1” symbol PSK
a(t)
Lightwave
carrier
FIGURE 1.8
Illustration of ASK, PSK, and FSK with the symbol and variation of the optical carrier (a) ampli-
tude, (b) phase, and (c) frequency.

(b) (c)Im ImIm
Re ReRe
Binary PSK QPSK 8 PSK
(a)
(e)(d) (f)
16 QAM 32 QAM
64 QAM
FIGURE 1.9
Constellations of the inphase and quadrature phases of lightwave carrier under modulation
formats (a) with π phase shift of the BPSK at the edge of the pulse period, (b) QPSK, (c) 8 PSK,
(d) 16 QAM with three rings, (e) 32 QAM, and (f) 64 QAM.
100
10–2
10–4
BER
10–6
10–8
Theoretical-offset QPSK
Theoretical-8 QAM
Theoretical-16 QAM
Theoretical-32 QAM
Theoretical-exact4
Eb/N0 (dB)
0 5 10 15 20 25 30
FIGURE 1.10
BER versus SNR for multi-level M-ary-QAM.

15Overview
the integrated PDM IQ-modulator, which can be fabricated on the LiNbO3
substrate for multiplexing the polarized modes and modulating both the
inphase and quadrature phase components. We have witnessed tremendous
development of transmission using such modulators over the last decade.
Besides these formats, the pulse shaping does also play an important part in
these advanced systems; the need to pack more channels for a given limited
C-band motivates several research groups in the exploitation of the employ-
ment of partial signal technique, such as the duobinary or vestoigial single-
side band and Nyquist pulse shaping.
They include nonreturn-to-zero (NRZ), return-to-zero (RZ), and duobinary
(DuoB). RZ and NRZ are of binary-level format, taking two levels “0” and
“1,” while DuoB is a tri-level format, taking the values of “−1 0 1.” The −1
in optical waves can be taken care of by an amplitude of “1” and a phase of π
phase shift with respect to the “+1,” which means a differential phase is used
to distinguish between the +1 and −1 states.
The modulated lightwaves at the output of the optical transmitter are then
fed into the transmission fibers and fiber spans, as shown in Figure 1.7.
1.3.2.2 Nyquist Pulse Shaping
One way to shape the pulse sequence is to employ the Nyquist pulse-shaping
techniques; that is, the pulse spectrum must satisfy the three Nyquist cri-
teria. Considering the rectangular spectrum with a sinc, that is ((sin x)/x),
time-domain impulse response, at the sampling instants t = kT (k = 1,2…, N
as nonzero integer) its amplitudes reach zero, implying that at the ideal sam-
pling instants, the ISI from neighboring symbols is thus negligible, or free of
intersymbol interference (ISI). Figure 1.11 depicts such Nyquist pulse and
its spectrum for either a single channel or multiple channels. Note that the
maximum of the next pulse raise is the minimum of the previous impulse of
the consecutive Nyquist channel.
Now considering one sub-channel carrier 25 GBaud PDM-DQPSK signal,
then the resulting capacity is 100 Gbps for a sub-channel, hence to reach
1 Tbps, 10 sub-channels would be required. To increase the spectral efficiency,
the bandwidth of these 10 sub-channels must be packed densely together.
The most likely technique for packing the channel as close as possible in the
frequency with minimum ISI is the Nyquist pulse shaping. Thus the name
Nyquist-WDM system is used. However, in practice, such “brick-wall-like”
spectrum shown in Figure 1.11 is impossible to obtain, and hence a nonideal
solution for non-ISI pulse shape should be found so that the raise cosine pulse
with some roll-off property condition can be met.
The raised-cosine filter is an implementation of a low-pass Nyquist filter,
that is, one that has the property of vestigial symmetry. This means that its
spectrum exhibits odd symmetry, about 1 2/ Ts , where Ts is the symbol-period.
Its frequency-domain representation is a brick-wall-like function, given by


H f
T
T T
f
T
fs
s s
s
( ) cos= + −
−
























≤
2
1
1
2
0
1
p
b
b
−−
−
≤
+
≤ ≤
b
b b
b
2
1
2
1
2
0 1
T
T
f
T
s
s s
otherwise
with

(1.2)
This frequency response is characterized by two values: β, the roll-off fac-
tor, and Ts, the reciprocal of the symbol rate in Sym/s, that is 1/2Ts, which is
the half bandwidth of the filter. The impulse response of such a filter can
Rs
Rs
Ts
Ts
t
t
t
t
Ts
Ts
f
f
(a) (b)
(c)
FIGURE 1.11
A super-channel Nyquist spectrum and its corresponding “impulse” response (a) spectrum,
(b) impulse response in time domain of a single channel, and (c) sequence of pulse to obtain
consecutive rectangular spectra. A superposition of these pulse sequences would form a rect-
angular “brick wall-like” spectrum.

17Overview
be obtained by analytically taking the inverse Fourier transformation of
Equation 1.2, in terms of the normalized sinc function, as

h t
t
T
t T
t Ts
s
s
( )
cos
( )
=




( )
− ( )
sinc
pb
pb
/
/1 2
2

(1.3)
where the roll-off factor, β, is a measure of the excess bandwidth of the fil-
ter, that is, the bandwidth occupied beyond the Nyquist bandwidth as from
the amplitude at 1/2T. Figure 1.12 depicts the frequency spectra of a raised
cosine pulse with various roll-off factors. Their corresponding time domain
pulse shapes are given in Figure 1.13.
When used to filter a symbol stream, a Nyquist filter has the property of
eliminating ISI, as its impulse response is zero at all nT (where n is an inte-
ger), except when n = 0. Therefore, if the transmitted waveform is correctly
sampled at the receiver, the original symbol values can be recovered com-
pletely. However, in many practical communications systems, a matched
Excess band
H( f )
f
β = 0
β = 0.25
β = 0.5
β = 1
– –1
T
1
T
1 0
2T
1
2T
FIGURE 1.12
Frequency response of a raised-cosine filter with various values of the roll-off factor β.
h(t)
–3T –2T –T T 2T 3T
t
0
β = 0
β = 0.25
β = 0.5
β = 1
FIGURE 1.13
Impulse response of a raised-cosine filter with the roll-off factor β as a parameter.

filter is used at the receiver, so as to minimize the effects of noises. For zero
ISI, the net response of the product of the transmitting and receiving filters
must equate to H(f), thus we can write:

H f H f H fR T( ) ( ) ( )=
(1.4)
Or alternatively, we can rewrite that

H f H f H fR T( ) ( ) ( )= =

(1.5)
The filters that can satisfy the conditions of Equation 1.5 are the root-raised-
cosine filters. The main problem with root-raised-cosine filters is that they
occupy larger frequency bands than that of the Nyquist sinc-pulse sequence.
Thus, for the transmission system we can split the overall raised cosine filter
with the root-raise cosine filter at both the transmitting and receiving ends,
provided the system is linear. This linearity is to be specified accordingly. An
optical fiber transmission system can be considered linear if the total power
of all channels is under the nonlinear SPM threshold limit. When it is over
this threshold, a weakly linear approximation can be used.
The design of a Nyquist filter influences the performance of the overall
transmission system. Oversampling factor, selection of roll-off factor for dif-
ferent modulation formats, and FIR Nyquist filter design are key parameters
to be determined. If taking into account the transfer functions of the overall
transmission channel, including fiber, WSS, and the cascade of the transfer
functions of all O/E components, the total channel transfer function is more
Gaussian-like. To compensate this effect in the Tx-DSP, one would thus need
a special Nyquist filter to achieve the overall frequency response equiva-
lent to that of the rectangular or raised cosine with roll-off factors shown in
Figure 1.13. The spectra of data sequences for which pulse shapes follow a
rectangle and a sinc function are shown in Figure 1.14a and b. The spectrum
of a pulse sequence of the raised cosine function shows its close approxima-
tion to a sinc function. This will allow effective packing of adjacent informa-
tion channels and transmission.
1.4 Optical Demodulation: Phase and Polarization
Diversity Technique
A generic schematic of the transmission is depicted in Figure 1.7. The output-
transmitted signals that are normally distorted are then detected by a digi-
tal optical receiver. The main function of this optical receiver is to recognize

19Overview
(a)
1
0.8
Nyquistfilter
Nyquistfilter
SORT-Nyquistfilter
Root-Nyquistfilter
–3dB
–6dB
–0.5
Normalizedfrequency
0.5
f
0.6
0.4
Amplitude
0.2
0
–0.2
–3–2–10
T/Ts
123
(b)
FIGURE1.14
(a)Impulseand(b)correspondingfrequencyresponseofsincNyquistpulseshapeorroot-raisecosine(RRC)Nyquistfilters.

whether the current received and therefore the “bit symbol” voltage at the
output of the amplifiers following the detector is a “1” or “0.” The modula-
tion of amplitude, phase, or frequency of the optical carrier requires an optical
demodulation. That is, the demodulation of the optical carrier is implemented
in the optical domain. This is necessary due the extremely high frequency of
the optical carrier (in order, or nearly 200 THz for 1550 nm wavelength); it is
impossible to demodulate in the electronic domain by direct detection using a
single photo-detector. The second most common technique is coherent detec-
tion by mixing the received signals with a local oscillator laser. The beating
signal in photodetection with square law application would result in three
components: one is the DC component, and the other two located at the sum-
mation and the difference of the two lightwave frequencies. Tone, thus, is very
far away in the electrical domain and only the difference component would
be detected in the electrical domain provided that this difference is within
the bandwidth of the electronic detection and amplification. Indeed, it is quite
straightforward to demodulate in the optical domain using optical interferom-
eters to compare the phases of the carrier in two consecutive bits for the case
of differential coding, which is commonly used to avoid demand on absolute
stability of the lightwave carrier.
However, the phase and frequency of the lightwave signals can be recov-
ered via an intermediate step by mixing the optical signals with a local oscil-
lator, a narrow linewidth laser, to beat it to the baseband or an intermediate
frequency region. This is known as the coherent detection technique. Figure
1.15 shows the schematics of optical receivers using direct detection and
coherent detection. If both polarization modes of the fiber line are employed,
then a 90° hybrid coupler would be used to split and mix the polarization of
both the received channels and the local oscillator. Further, the optical fre-
quency regions of the lightwaves employed for optical communications are
indicated in Figure 1.16. In this case, the terms polarization and phase diver-
sity coherent detection can be used. As we can see, 4 pairs of photodetectors
are connected back to back as balanced detectors. They are required for detec-
tion of two polarized channels and two pairs of the in-phase and quadra-
ture components of the QAM modulated channels. The received signals are
sampled by an ultra-high speed analog to digital converter (ADC) and then
processed in realtime by algorithms stored a DSP. Figure 1.17 shows generic
flow diagram of the algorithm which are commonly employed in the digital
processing of transmitted signals. Figure 1.18 shows the schematic diagram
of a DSP-based coherent optical receiver in which both the analog and digital
processing parts are included.
The main difference between these detection systems and those presented in
several other textbooks is the electronic signal processing sub-system follow-
ing the detection circuitry. In the first decade of this century we have witnessed
tremendous progress in the speed of electronic ultra-large-scale integrated cir-
cuits, with the number of samples per second now reaching a few tens of GSa/s.
This has permitted considerations for applications of DSP of distorted received

21Overview
OpticalTX+pulse
shaping
Fiberandoptical
amplifiers
transmissionspans
Detection
optical-electronic
domain
Electronic
amplification
+
DSPanddata
recovery
Precoderformapping
tomodulationscheme
Binarydatagenerator
bit-patterngen.
(a)
(b)
Optical
transmitter
Optical
receiver
Opticalfilter
(e.g.,mux)
Opticalfilter
(e.g.,mux)
Opticalamplifier
Optical
transmissionfiber
Opticaldispersion
compensationfiber
×Nspans
FIGURE1.15
(a)Generalizeddiagramofdispersion-managedopticaltransmissionsystems;(b)moredetailsofthedispersionmanagementofmulti-spanlink.

Frequency
(Hz)
wavelength
1e2 1e4 1e6 1e8 1e10 1e12 1e14 1e16 1e18
Microwave
millimeterwave
Far
infrared X-ray Gamma-
ray
Infrared 1550 nm
S-, C-, and L-bands
FIGURE 1.16
Electromagnetic spectrum of waves for communications, and lightwaves region for silica-
based fiber optical communications.
Transmitted/received optical signals
optical-electrical conversion via balance
reception/phase-polarization diversity optical
frnt end/optoelectronic conversion
Analog to digital converter
(4 channels for QAM signals)
Waveform recovery and alignment of
sampled signals
Dispersion compensation
Carrier phase/clock recovery
Synchronized data re-sampling
Multi-stage constant modulus algo
(CMA)
Single-stage CMA
LO frequency offset compensation LO frequency offset compensation
Carrier phase estimation Carrier phase estimation
Maximum likelihood sequence estimation
BER estimation/
recovery data sequence (real time)
Real-time
or
offline processing
from here onwards
FIGURE 1.17
Flow chart of block schematic of the optical digital receiver and DSP.

23Overview
optical signals in the electronic domain. Thus, flexibility in the equalization of
signals in transmission systems and networks is very attractive.
1.5 Organization of the Book Chapters
The chapters of this book are dedicated to the latest development in research
and practical systems to date. The presentation of this book follows the inte-
gration of optical components and digital modulation and DSP techniques in
coherent optical communications in the following manner.
Chapter 2 briefly summarizes the fundamental properties of the waveguid-
ing phenomena, especially the polarization modes and few mode aspects in
optical fibers and essential parameters of such waveguides that would influ-
ence the transmission and propagation of optical modulated signals through
the circular optical waveguide. This chapter presents the static parameters,
including the index profile distribution and the geometrical structure of the
fiber, the mode spot size and mode field diameter of optical fibers, and thence
the estimation of the nonlinear self-phase modulation effects. Operational
parameters such as group velocity, group velocity dispersion, and disper-
sion factor and dispersion slope of single-mode fibers as well as attenuation
factors are also given. The frequency responses, including impulse and step
responses, of optical fibers are also given, so that the chirping of an opti-
cally modulated signal can be understood from the point of view of phase
evolution when propagating through an optical fiber, a quadratic phase
modulation medium. The propagation equation, the nonlinear Schroedinger
equation (NLSE) that represents the propagation of the complex envelope of
the optical signals, is also described so that the modeling of the signal propa-
gation can be related.
Chapter 4 describes the optical receiver configurations based on principles
of coherent reception and the concepts of polarization, phase diversity, and
Electronic
pre- and main
amplifiers
High speed
sampling
ADC +
digital
decision
circuitry
Local
oscillator
(LO laser)
Optical mixer/
90° hybrid
coupler
Electronic
DSP
equalization
and phase
detection
4 × PDP
FIGURE 1.18
Schematics of optical receivers employing coherent detection and DSP. PDP = photodetector
pair connected back to back.

DSP technique. A local oscillator (LO) is required for mixing with the spec-
tral components of the modulated channel to recover the signals back to the
base band. Any jittering of the central frequency of the LO would degrade
the system performance. The DSP algorithms in real time will recover the
carrier phase, but only within a certain limit or tolerance of the carrier fre-
quency. Thus, an optical phase locking may be required. This technique is
presented in Chapter 5.
Chapter 6 outlines the principles of DSP and associated algorithms for dis-
persion compensation, carrier phase recovery, and nonlinear equalization
by Volterra transfer functions and back propagation, Nyquist post filtering,
and pre-filtering.
Chapter 7 then gives detailed designs, experimental and field demonstra-
tions, and transmission performance of optical transmission systems employ-
ing DSP technique.
Chapter 8 introduces processing techniques in frequency domain, employ-
ing higher-order spectral techniques for both DSP-based coherent receivers
and photonic processing, incorporating nonlinear optical waveguides for
optical multi-dimensional spectrum identification.
References
1. C. Kao and G. Hockham, Dielectric-fibre surface waveguides for optical fre-
quencies, Proc. IEE, 113(7), 1151–1158, 1966.
2. Maurer et al., Fused silica optical waveguide. U.S. Patent 3,659,915 (1972–05).
3. Keck, IV Method of producing optical waveguide fibers. U.S. Patent 3,711,262
(1973–01).

25
2
Optical Fibers: Guiding and
Propagation Properties
2.1 Optical Fibers: Circular Optical Waveguides
2.1.1 General Aspects
Planar optical waveguides compose a guiding region, a slab imbedded
between a substrate and a superstrate having identical or different refrac-
tive indices. The lightwaves are guided by the confinement of the lightwaves
with oscillation solution. The number of oscillating solutions that satisfy the
boundary constraints is the number of modes that can be guided. The guid-
ing of lightwaves in an optical fiber is similar to that of the planar wave-
guide, except the lightwaves are guiding through a circular core embedded
in circular cladding layer.
Within the context of this book, optical fibers would be most relevant
as the circular optical waveguides that can support single mode with two
polarized modes or few modes with different polarizations. We should point
out the following development in optical fiber communications systems.
• Step-index and graded index multimode optical fibers find very lim-
ited applications in systems and networks for long-haul applications.
• Single-mode optical fibers have structured with very small differ-
ence in the refractive indices between the core and cladding regions.
Thus, the guiding in modern optical fiber for telecommunications
is called “weakling” guiding. This development was intensively
debated and agreed upon by the optical fiber communications tech-
nology community during the late 1970s.
• The invention of optical amplification in rare-earth doped, single-
mode optical fibers in the late 1980s has transformed the design and
deployment of optical fiber communications systems and networks
in the last decade and the coming decades of the twenty-first cen-
tury. The optical loss of the fiber and the optical components in the

optical networks can be compensated for by using these fiber in-line
optical amplifiers.
• Therefore, the pulse broadening of optical signals during transmis-
sion and distribution in the networks becomes much more impor-
tant for system design engineers.
• Recently, due to several demonstrations of the use of digital sig-
nal processing of coherently received modulated lightwaves, mul-
tiple input-multiple output (MIMO) techniques can be applied to
enhance significantly the sensitivity of optical receivers and thus
the transmission distance and the capacity of optical communication
systems [1]. MIMO techniques would offer some possibilities of the
uses of different guided modes through a single fiber, for example,
few mode fibers that can support more than one mode but not too
many, as in the case of multimode types. Thus the conditions under
which circular optical waveguides can operate as a few-mode fibers
are also described in this chapter.
Owing to the above development we shall focus the theoretical approach
to the understanding of optical fibers on the practical aspects for designing
optical fibers with minimum dispersion or for a specified dispersion factor.
This can be carried out by, from practical measurements, the optical field dis-
tribution that would follow a Gaussian distribution. Knowing the field dis-
tribution, one would be able to obtain the propagation constant of the single
guided mode, the spot size of this mode, and thus the energy concentration
inside the core of the optical fiber. The basic concept of optical dispersion by
using the definition of group velocity and group delay we would be able to
derive the chromatic dispersion in single-mode optical fibers. After arming
ourselves with the basic equations for dispersion we would be able to embark
on the design of optical fibers with a specified dispersion factor.
2.1.2 Optical Fiber: General Properties
2.1.2.1 Geometrical Structures and Index Profile
An optical fiber consists of two concentric dielectric cylinders. The inner cyl-
inder, or core, has a refractive index of n(r) and radius a. The outer cylinder,
or cladding, has index n2 with n(r) n2 and a larger outer radius. A core of
about 4–9 μm and a cladding diameter of 125 μm are the typical values for
silica-based single-mode optical fiber. A schematic diagram of the structure
of a circular optical fiber is shown in Figure 2.1. Figure 2.1a shows the core
and cladding region of the circular fiber, while Figures 2.1b and 2.1c show the
figure of the etched cross sections of a multimode and single mode, respec-
tively. The silica fibers are etched in a hydroperoxide solution so that the core
region doped with impurity would be etched faster than that of pure silica,
thus the exposure of the core region as observed. Figure 2.2 shows the index

27Optical Fibers
(a)
Core
Cladding
(b) (c)
FIGURE 2.1
(a) Schematic diagram of the step-index fiber: coordinate system, structure. The refractive
index of the core is uniform and slightly larger than that of the cladding. For silica glass, the
refractive index of the core is about 1.478 and that of the cladding about 1.47 at 1550 nm wave-
length region. (b) Cross-section of an etched fiber—multimode type—50 micrometer diameter.
(c) Single-mode optical fiber etched cross-section.
r2(r)
Graded distribution
CladdingCladding
(a)
(b)
Cladding
Core2d
Step index
profile
n1
n2
n2
Core
n2
z
n2
Radial direction
Propagation
direction
+a–a
n1
FIGURE 2.2
(a) Refractive index profile of a graded index profile; (b) fiber cross-section and step index pro-
file with a as the radius of fiber.

profile and the structure of circular fibers. The refractive index profile can be
step or graded.
The refractive index n(r) of a circular optical waveguide is usually changed
with radius r from the fiber axis (r = 0) and is expressed by

n r n NA s
r
a
2
2
2 2
( ) = +





(2.1)
where NA is the numerical aperture at the core axis, while s(r/a) represents
the profile function that characterizes any profile shape (s = 1 at maximum)
with a scaling parameter (usually the core radius).
For a step-index profile, the refractive index remains constant in the core
region, thus

s
r
a
r a
r a
n r
n r a
n r
hence
ref index


 =
≤





 → =
≤1
0
2
1
2
2
2
_
( )




 a

(2.2)
For a graded-index profile, we can consider the two most common types of
graded-index profiles: power-law index and the Gaussian profile.
For power-law index profile, the core refractive index of optical fiber is
usually following a graded profile. In this case, the refractive index rises
gradually from the value n2 of the cladding glass to value n1 at the fiber axis.
Therefore, s(r/a) can be expressed as

s
r
a
r
a
r a
r a



 =
−



 ≤






1
0
a
for
for

(2.3)
with α as power exponent. Thus, the index profile distribution n(r) can be
expressed in the usual way, by using Equations 2.3 and 2.2, and substituting
NA n n2
1
2
2
2
= − .

n r
n
r
a
r a
n r a
2 1
2
2
2
1 2
( ) =
−












≤






∆
α
for
for

(2.4)
∆ = ( )NA n2
1
2
/ is the relative refractive difference with small difference
between that of the cladding and the core regions. The profile shape given
in Equation 2.4 offers three special distributions: (i) α = 1: the profile function
s(r/a) is linear and the profile is called a triangular profile; (ii) α = 2: the profile

Book

Recommended

Recommended

More Related Content

Viewers also liked

Viewers also liked (17)

Similar to Book

Similar to Book (20)

More from Ali Azarnia

More from Ali Azarnia (9)

Recently uploaded

Recently uploaded (20)

Book